The historical drama film *The Imitation Game* is about Alan Turing breaking the German wartime Enigma code. To solve the code, Alan Turing applied Bayes’ approach to probability, which has been termed “the theory that would not die.” The Bayesian interpretation of probability reflects the incompleteness of our knowledge and is suited for mastering complexity (1). Bayes’ rule can be described in one sentence: by updating our initial beliefs (about something) with objective new information, we get a new and improved belief (2).

The mathematician George Pólya presented a powerful way of reasoning to discover the solution to a problem in his classic introduction to mathematical problem solving (3). He divides the process of problem-solving into four phases:

- Understand the problem.
- Consider related problems whose solutions are already known and use reason by analogy to devise a plan.
- Carry out the plan.
- Examine the solution obtained.

In medicine, the frequentist approach to probability has dominated research, partly because the method is useful to falsify a hypothesis. However, when it comes to solving a problem, the Bayesian approach to probability is by far a more efficient method.

If we assume that all diseases are caused by microorganisms (except genetically determined diseases, nutritional deficiencies, and injuries), a lot of microbes may cause disease in humans. There are 113 groups of bacterial organisms, families of DNA/RNA viruses, major classes of fungi, phyla of protozoa, and helminths (worms) of medical interest (4). Within these groups are a number of different species. A rough estimate of the major potential candidates for human disease therefore exceeds 200 species of microorganisms.

If we aim at unravelling which microorganisms cause myalgic encephalomyelitis/chronic fatigue syndrome (ME/CFS), we may assume that the microorganism that causes ME/CFS is among these 200 species. Taking the frequentist approach, there are 200 hypotheses about the cause of ME/CFS and all of them have the same probability of being correct, i.e., 1 in 200. Each of the hypotheses must be tested and falsified – one by one – until one of them is not falsifiable.

By applying the Bayesian approach, we may take our knowledge about these microorganisms into account and use our subjective beliefs about the probability of the 200 different microorganisms as possible causes of ME/CFS. Any knowledge relevant to the problem may be taken into account to estimate the prior or pre-test probability of the 200 hypotheses.

First, ME/CFS is a disease that is not transmittable between humans. Therefore, the infectious microorganisms causing ME/CFS are probably transmitted from animals (zoonoses) or from vectors such as ticks and mosquitoes (vector-borne diseases). Most vector-borne microorganisms that cause diseases are not foundin the rich part of the world, except the bacterium *Borrelia burgdorferi*. However, the extent to which an infection with this bacterium may cause ME/CFS has been researched and the conclusion so far is that the infection cannot explain ME/CFS. If we take this information into accout, the Bayesian approach to *Borrelia burgdorferi* as a cause of ME/CFS is to consider it less probable – rather than continue torturing this bacterium until it confesses.

For these reasons, a great number of infectious microorganisms, such as nearly all viruses, bacteria, and protozoa (single-cell microorganisms), can be considered as improbable causes of ME/CFS.

Second, of the zoonoses, the most probable infectious causes of ME/CFS are among those microorganisms that are exclusively transmittable from animals and not transmittable between humans. Infectious microorganisms with a life cycle that includes two or more hosts are not communicable between humans. Most of these microorganisms are found only in the tropics and can be considered as improbable causes of ME/CFS among patients in the rich part of the world. The only parasites found worldwide with a life cycle that includes two or more hosts are *Toxoplasma gondii*, *Toxocara* spp., *Echinococcus granulosus*, and *Taenia* spp. with dogs and cats as their definitive hosts.

Hence, by this simple Bayesian reasoning, the pre-test probability of finding the cause of ME/CFS among these parasites is immensely higher compared with the pre-test probability of finding the cause among the remaining 200 microorganisms.

Furthermore, Bayesian reasoning may be applied to estimate the pre-test probability of each of these parasites as the cause of ME/CFS. If we use the listing in PubMed for these parasites as a proxy for knowledge, *Toxoplasma gondii* has been most extensively studied and has 15579 publications (30 December 2014). The numbers for *Echinococcus* are 6110 publications, and for *Toxocara* spp. 2886 publications. The *Taenia* species with dogs or cats as their definitive host are highly neglected. The numbers of papers for them are as follows: *Taenia crassiceps* 494, *Taenia ovis* 417, *Taenia hydatigena* 346, *Taenia taeniaeformis* 322, *Taenia pisiformis* 180, *Taenia multiceps* 119, *Taenia serialis* 43, and *Taenia martis* 18. Reports of the other more than 30 *Taenia* species with dogs as their definitive host are non-existent in PubMed.

This information may be taken into account in Bayesian reasoning because it is reasonable to suppose that the unknown cause of a disease will be found among less extensively studied microorganisms rather than among those that have been extensively studied. My conclusion, therefore, in accordance with Bayesian reasoning, is that the pre-test probabilities of these parasites as the cause of ME/CFS are as follows.

**Highest pre-test probability:** *Taenia* species with dogs or cats as their definitive host.

**Second highest pre-test probability:** *Toxocara* species with dogs or cats as their definitive host.

Lower pre-test probability: *Echinococcus granulosus.*

Lowest pre-test probability: *Toxoplasma gondii.*

References:

- Mahajan S. The art of insight in science and engineering. The MIT Press, 2014. p.235
- McGrayne SB. The theory that would not die: how Bayes’ rule cracked the enigma code, hunted down Russian submarines and emerged triumphant from two centuries of controversy. Yale University Press, 2011.
- Pólya G. How to solve it. A new aspect of mathematical method. Princeton University Press, 2014 (original work published by Princeton University Press, 1945).
- Murray PR, Rosenthal KS, Pfaller MA. Medical microbiology. 7th edition. Elsevier, 2013.